DeWitt Payne has done an interesting post here regressing ice core CO2 and deuterium temperature proxy information to examine the plausibility of CO2 amplification of temperature swings between ice ages. This is a favorite point of climate naturalists 🙂 regarding temperature swings in distant history, however there may be an explanation. Read on with an open mind, because physics doesn’t care what we think. -Jeff Id
On The Relationship of CO2 and Deuterium Isotope Shift in the Dome C Ice Core
An understanding of the fundamentals of the standard hypothesis of what is called the atmospheric greenhouse effect is required to be able to concentrate on the true uncertainties. Proponents of a high climate sensitivity to doubling of atmospheric CO2 concentration claim that a high sensitivity is required to explain the magnitude of the temperature change from glacial to interglacial conditions. The shift in climate is thought to be triggered by small changes in insolation at high latitudes caused by cyclic changes in the Earth’s orbital parameters (Milankovitch cycles).
However, the size of the change in insolation is not sufficient according to the standard hypothesis to cause a temperature shift of the size observed. I have a problem with the assumption in the link above that interglacial climate conditions are stable and a decrease in insolation is required to trigger an ice age, but that’s not what I want to discuss here. Some mechanism or combination of mechanisms is required to amplify temperature change. The two main contributors are thought to be ice/albedo feedback and CO2.
We know with reasonable confidence from measurements of atmospheric samples trapped in bubbles in ice cores that CO2 is correlated with temperature as determined by the shift in deuterium/hydrogen isotope ratio. We also know with reasonable confidence from atmospheric radiation transfer theory and the characteristics of the infra-red absorption spectrum of CO2 that atmospheric CO2 acts to increase the surface temperature of the planet compared to a planet with no atmosphere.
However, the ice core measurements have CO2 concentration changes lagging temperature. Is amplification of temperature change by CO2 still plausible? Arguments against significant climate sensitivity for CO2 as demonstrated by ice core data include:
1. The change in CO2 concentration is an effect of temperature with a significant time lag so it can’t affect the temperature.
2. If CO2 really does amplify the temperature increase, the onset of the amplification should be obvious when temperature and CO2 are plotted on the same graph.
I will demonstrate that amplification of temperature change by CO2 is indeed plausible even though changes in CO2 concentration follow temperature rather than lead.
CO2 as a function of deltaD
Dome C deuterium isotope shift data1 can be found at the NOAA Paleoclimatology Program web site: ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/epica_domec/edc_dd.txt
Dome C CO2 concentration data2 can be found on the same web site:
I’m not going to try to convert deltaD to temperature because it doesn’t represent a global temperature. I do assume that deltaD is proportional to global temperature. I also assume that equilibrium CO2 concentration is a linear function of deltaD, but the actual concentration lags behind the equilibrium concentration with a time constant of tau. CO2 concentration at time t will be a function of the CO2 concentration at time t will be a function of the CO2 concentration at t-1 plus the difference between the calculated equilibrium CO2 concentration (CO2e) at time t and the CO2 concentration at t-1 multiplied by a time lag factor: (1-exp(-(delta t)/tau).
CO2e(t) = m*deltaD(t)+k
The CO2 data and the deltaD data are not simultaneous. A deltaD data set that matched the times of the CO2 data set was created by linear interpolation between the values with dates that bracketed the CO2 dates. Then the Excel Solver function was used to minimize the sum of the squares of the differences between the calculated CO2 concentration and the measured concentration by varying m, k and tau. The result was:
m = 1.98225
k = 1062.88
tau = 2496.272
A regression of CO2 calculated vs. CO2 measured had an R squared of 0.98, an F statistic of 4037 and a slope and intercept that were not significantly different from 1 and 0 respectively. Using all the deltaD data from 30,000 years BP gave a concentration of CO2 at 70 years BP of 276 ppmv.
Contribution to the change of deltaD with time from CO2
Jeff Severinghaus, professor of geosciences at Scripps Institution of Oceanography, succinctly explains:
The contribution of CO2 to the glacial-interglacial coolings and warmings amounts to about one-third of the full amplitude, about one-half if you include methane and nitrous oxide.
The change in deltaD over the time scale of the Dome C CO2 data is 45.4 ppm. Assume that 30% of that change is due to CO2. Also assume that the change in deltaD is proportional to the logarithm of the ratio of the concentration of CO2 at time t to the initial CO2 concentration:
Thirty percent of the change in deltaD is 13.62 ppm. Initial CO2 concentration is 184.4 ppmv and the final concentration is 265.2 ppmv. Solving equation 3 for a gives a=37.5. Subtracting the change due to CO2 from the measured deltaD gives:
The basic form of the corrected deltaD curve is still about the same. The dip from the Antarctic Cold Reversal, that is about 1000 years earlier than the similar dip in Northern Hemisphere temperatures known as Younger Dryas, is somewhat enhanced. Acceleration of warming is only obvious because both results are plotted on the same graph.
Modeling CO2 as effect and amplifier
The measured data is noisy and the Antarctic Cold Reversal dip is an additional complication. Starting with a sigmoid forcing with no CO2 feedback similar in magnitude to that observed in the Dome C core with time steps of 100 years and the constants adjusted to give a curve with similar characteristics to the corrected deltaD curve above:
Then use Equation 1 to calculate CO2 concentration from the synthetic deltaD data gives:
Then use equation 3 to calculate the increase in deltaD from the calculated CO2 concentration and add that to the initial deltaD to produce deltaD fb1. Use the deltaD fb1 to calculate CO2 again and continue the process until the difference between iterations is no longer significant. I stopped after five iterations when the difference in the final CO2 concentration was less than 0.1 ppmv.
There is a subtle difference in shape and position of the deltaD with feedback curve compared to the no feedback curve, but it’s not at all obvious even with noise free data. If I fit a sigmoid curve to the deltaD with feed back curve I get this:
The fitted equation is:
Compare the constants in this equation to those in Equation 4.
There is no problem with the math for CO2 being both an effect and amplifier of temperature. There is also no problem with amplification when there is a time lag between the increase in temperature and increase in CO2. Given the time it takes to transfer heat to the deep ocean, which contains the bulk of dissolved CO2, a time constant of 2500 years is not at all unreasonable. A long time constant for oceanic CO2 evolution also supports the hypothesis that the recent increase in CO2 is from the burning of fossil carbon as the increase in temperature in the last 100 years would have had little effect on atmospheric CO2.
On the other hand, this is a double edged sword. While you can’t prove that CO2 didn’t amplify warming unless you know the precise shape of the underlying forcing, you also can’t prove that it did amplify warming or determine the magnitude of the effect and hence the climate sensitivity to doubling CO2 concentration for exactly the same reason. There are other known and possible feedbacks. Ice/albedo is probably the largest known. However, it is much less well understood than the greenhouse effect as it varies strongly with the latitude of the ice edge, not to mention the varying albedo of different kinds of ice, whether it’s snow covered or not or the effect of dust deposits. In addition, the contributions from clouds and aerosols are uncertain. Then there are the don’t don’ts, the things we don’t know we don’t know. So I’m not at all impressed with the argument that the climate sensitivity to CO2 must be high because glacial-interglacial transitions can’t be modeled without high climate sensitivity for CO2.
1. Jouzel,J., et al. 2004. EPICA Dome C Ice Cores Deuterium Data. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series #2004-038. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.)
2. Monnin et al. Science v.291 pp112-114